Abstract

In this paper we introduce a novel family of semantics called weakly complete semantics, unlike Dung's complete semantics, weakly complete semantics use a mechanism termed undecidedness blocking. This mechanism prevents the propagation of the 'undecided' label of an attacking argument to a previously accepted argument. The weakly complete semantics are conflict-free, non-admissible but deploying a weaker concept of admissibility. These semantics allow for the reinstatement of arguments and maintain the majority of the properties of complete semantics. By applying various undecidedness blocking strategies, both the weakly complete and Dung's complete semantics can be generated, making undecidedness blocking a common mechanism that underpins argumentation semantics. Lastly, we present a comparison of the weakly complete semantics with the recent work of Baumann et al.on weakly admissible semantics and provide a principle-based analysis of both.

1. Introduction

Abstract argumentation is a reasoning framework where conclusions are reached by evaluating arguments and their conflict relation. One of the main tasks of abstract argumentation is the computation of the acceptance status of arguments, identified as extensions, which survive the conflicts in the attack relation. In the labelling approach, every argument is assigned a label as in, out, or undecided.

In this paper, we introduce weakly complete semantics, a new family of abstract semantics. The unique feature of these semantics is their use of undecidedness blocking. In contrast, in Dung's complete semantics, the propagation of the 'undecided' label is always allowed. We delve into a principle-based analysis of these new semantics and then draw a comparison with Baumann et al.'s weakly admissible semantics.

We propose these new semantics for two reasons: firstly, to include the fundamental reasoning mechanism of ambiguity blocking, which is currently absent in abstract semantics, and secondly, to propose semantics that can solve the 25-year old problem of self-defeating attacking arguments.

Motivation 1: Ambiguity Blocking and Abstract Argumentation

Ambiguity blocking semantics are used in various non-monotonic formalisms, such as defeasible logic. The ambiguity blocking mechanism invalidates any statements that possess contradictory evidence regarding their validity and does not influence the validity of other statements. However, translating the ambiguity blocking mechanism into Dung's framework is not simple as the concept of ambiguity is not even defined in Dung's framework. This paper aims to introduce a new abstract semantics which directly incorporates ambiguity blocking rather than replicating the behavior through additional arguments.

Motivation 2: The Weak Attacks Problem

Self-defeating arguments pose significant problems in Dung's framework. Although this problem has been discussed by researchers like Baumann et al, these new semantics are the first to handle these problems. The blocking of undecidedness semantics provides a different solution to 'which arguments are weak enough to be neglected'. Both these semantics and BBU semantics remove the admissibility property of Dung's semantics.

The undecidedness blocking semantics handle all the motivating examples provided, while the BBU semantics do not address all problems. Our semantics offer an interpretation where variations of the same situation, an argument attacked by a self-contradicting argument, are treated identically, as per ambiguity blocking semantics.